1. Field of the Invention
The present invention relates to a wavelength converter which receives laser light of the fundamental wave from a semiconductor laser, and produces the second harmonic of the fundamental wave in the form of wavelength-converted light.
2. Discussion of the Prior Art
A wavelength converter is known which receives the fundamental wave of laser light and produces the second harmonic as wavelength-converted light of the halved wavelength. There are two types of wavelength converters, a bulk crystal type element and a wave-guide type element. The wave-guide type includes wavelength converters of the optical fiber type and the channel type.
The bulk crystal type wavelength converter is easier to handle than the wave-guide type wavelength converter because it is easy to direct laser beams to the wavelength converter, and a beam pattern of the generated second harmonic is the same as that of the incident laser beams.
The bulk crystal type wavelength converter will be described in more detail. A fundamental wave of the angular frequency .omega. is applied to the end face 2 of a bulk crystal wavelength converter 1 as shown in FIG. 2 (PRIOR ART). An electric field E.sub.2W of the generated second harmonic (angular frequency 2.omega.) is ##EQU1##
In formula (1), z indicates the linear coordinate in the incident direction of the fundamental wave, "d" indicates the nonlinear optical coefficient of the second degree and .DELTA.k is given by ##EQU2## k.sub.W =number of waves of the fundamental wave k.sub.2W =number of waves of the second harmonic
n.sub.W =refractive index of the crystal to the fundamental wave PA1 n.sub.2W =refractive index of the crystal to the second harmonic PA1 .lambda.=wavelength of the fundamental wave. From the formulas (1) and (2), we have ##EQU3## PA1 .epsilon..sub.0 =dielectric constant of vacuum PA1 P.sub.w =intensity of the fundamental wave PA1 w.sub.0 =beam radius of the fundamental wave
Then, an intensity P.sub.2W of the second harmonic is ##EQU4## (where E.sub.2W.sup.* is the complex conjugate of the electric field E.sub.2W). Where .DELTA.k.noteq.0, that is, when EQU n.sub.2W .noteq.n.sub.W ( 5)
which is derived from formula (2), the intensity P.sub.2W of the second harmonic periodically varies with respect to the z coordinate position, as indicated by a curve A1 in FIG. 3. The 1/2 period Lc of the intensity variation is defined as a coherent length and mathematically expressed by the following formula ##EQU5##
When .DELTA.k=0, that is, when, EQU n.sub.2W =n.sub.W ( 7)
which is derived from formula (2), we see that an intensity P.sub.2W of the second harmonic, from formula (4), is EQU P.sub.2W .varies.d.sup.2 L.sup.2 ( 8)
This indicates that the intensity of the second harmonic increases proportionally to the square of the crystal length L, as indicated by a curve A2 in FIG. 3. The physical state is called a phase matching. An intensity P.sub.2W of the second harmonic, which is generated in the state of the phase matching, is given by ##EQU6## where .mu..sub.0 =magnetic permeability of vacuum
To realize the phase matching, in the bulk crystal type wavelength converter, the crystal is sliced in a specific orientation by utilizing the optical anisotropy of the crystal the physical property of the crystal where the refractive index differs in different orientations when measured along the axes.
Thus, in the bulk crystal type wavelength converter, the phase matching is realized by utilizing the optical anisotropy of the crystal. Therefore, only the nondiagonal element d.sub.ij (i.noteq.j) of the nonlinear optical tensor is allowed to be used for the nonlinear optical coefficient "d" of second degree. Hence, the wavelength converting efficiency is low. Generally, the maximum element of the nonlinear optical tensor is frequently the diagonal element d.sub.ii. This diagonal element cannot be utilized in the bulk crystal type wavelength converter, however. Additionally, in the phase matching state, the non-diagonal element d.sub.ij cannot be fully utilized, hence a great increase in the wavelength converting efficiency cannot be expected.
A specific type of the bulk crystal type wavelength converter is the domain inverting type wavelength converter, as shown in FIG. 4 (PRIOR ART). This type of wavelength converter includes a diagonal element d.sub.ii of the nonlinear optical tensor, and may be utilized in the bulk crystal type wavelength converter. As shown, the domains 11 are layered alternately, inverting the directions (denoted as P) of the nonlinear optical coefficients "d". The thickness of each domain 11 is an odd number times as long as the coherent length Lc, i.e., mLc (m=odd number).
As described above, in a state that n.sub.2W .noteq.n.sub.W, where the phase matching is not realized, the intensity P.sub.2W of the second harmonic periodically varies. The periodical variation of the intensity is due to the fact that the phase difference of 2.pi. is present between the electric field E.sub.2W (z) generated at the coordinate position "z" on the linear coordinate, which lies in the incident direction of the fundamental wave, and the electric field E.sub.2W (z+Lc) generated at the coordinate position "(z+Lc)". Accordingly, the electric fields E.sub.2W cancel each other (particularly at the coordinate positions z=2Lc, 4Lc, the electric fields completely cancel each other).
If the electric field E.sub.2W of the second harmonic generated in the segment [z+Lc, z+2Lc] is inverted by .pi., the electric fields E.sub.2W (z) and E.sub.2W (z+Lc) do not cancel each other, and the intensity P.sub.2W of the second harmonic progressively increases. The .pi. phase inversion of the electric field E.sub.2W may be realized by inverting the sign of the nonlinear optical coefficient "d". Eventually, this indicates that the domains 11, each having a thickness which is an odd number times as long as the coherence length Lc, are layered in such a way that the directions of the nonlinear optical coefficients "d" of the domains are alternately inverted, as shown FIG. 4.
If ##EQU7## the electric field E.sub.2W, which is generated in the domain inverting type wavelength converter of length L, is: ##EQU8##
From formulas (2) and (6), we see that EQU Lc=.pi./.DELTA.k. (12)
Since "m" is an odd number, ##EQU9## Substituting formulas (10) and (12) into the above formula, we get ##EQU10## Therefore, an intensity P.sub.2W of the second harmonic is given by ##EQU11## When comparing formulas (15) and (8), if ##EQU12## it is seen that both formulas are exactly equal to each other. This implies that even if the phase matching condition according to formula (7) is not satisfied, the domain inverting type wavelength converter, as shown in FIG. 4, is able to generate the second harmonic, as the bulk crystal type wavelength converter does when the phase matching condition is satisfied. This is called a quasiphase matching. Since the optical anisotropy of the crystal is not utilized, a high efficiency wavelength conversion can be realized by utilizing the diagonal element d.sub.ii of the second degree, nonlinear optical tensor. An intensity P.sub.2W of the second harmonic in the domain inverting type wavelength converter is expressed by ##EQU13##
However, an excessive increase in the thickness of domain 11 results in a great attenuation of the second harmonic, limiting the wavelength converting efficiency. Therefore, the thickness of the domain 11 must be set to be about several .mu.m. It is very difficult to manufacture thin films of such thickness and to layer them in a manner that the directions of the nonlinear optical coefficient "d" are alternately inverted. Only several examples of the domain inverting type bulk crystal wavelength converter actually manufactured have thus far been reported. The number of the layers of those examples ranges only from several to twenty. Therefore, the wavelength converting efficiency is unsatisfactory. The wavelength converter, which utilizes the diagonal element d.sub.ii of the second degree, nonlinear optical tensor, has not yet been put into practice. Thus, it is very difficult to realize a bulky wavelength converter with high wavelength converting efficiency.